Generalizing the Nagel line to circumscribed polygons by analogy and constructive defining

dc.creator	Michael de Villiers
dc.date	2011-10-01T00:00:00Z
dc.date.accessioned	2015-07-20T22:10:19Z
dc.date.available	2015-07-20T22:10:19Z
dc.identifier	10.4102/pythagoras.v33i68.65
dc.identifier	1012-2346
dc.identifier	2223-7895
dc.identifier	https://doaj.org/article/e59e9bd78a9d426093a0c06579aab075
dc.identifier.uri	http://evidence.thinkportal.org/handle/123456789/13540
dc.description	This paper first discusses the genetic approach and the relevance of the history of mathematics for teaching, reasoning by analogy, and the role of constructive defining in the creation of new mathematical content. It then uses constructive defining to generate a new generalization of the Nagel line of a triangle to polygons circumscribed around a circle, based on an analogy between the Nagel line and the Euler line of a triangle.
dc.language	English
dc.publisher	AOSIS OpenJournals
dc.relation	http://www.pythagoras.org.za/index.php/pythagoras/article/view/65
dc.relation	https://doaj.org/toc/1012-2346
dc.relation	https://doaj.org/toc/2223-7895
dc.rights	CC BY
dc.source	Pythagoras, Vol 0, Iss 68, Pp 32-40 (2011)
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.title	Generalizing the Nagel line to circumscribed polygons by analogy and constructive defining
dc.type	article